A) \[{{30}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{60}^{o}}\]
D) \[~{{75}^{o}}\]
Correct Answer: B
Solution :
We have, \[(1+tan\theta )(1+tan\phi )=2\] \[\Rightarrow \] \[1+\tan \theta +\tan \phi \text{+}\,\text{tan}\theta \text{.tan}\phi \text{=}\,\text{2}\] \[\Rightarrow \] \[\tan \theta +\tan \phi =1-\tan \theta .\tan \phi \] \[\Rightarrow \] \[\frac{\tan \theta +\tan \phi }{1-\tan \theta .\tan \phi }=1\] \[\Rightarrow \] \[\tan (\theta +\phi )=tan\pi /4\] \[\theta +\phi \,=\pi /4={{45}^{o}}\]
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